Nuprl Lemma : path-comp-rel_wf
∀[X:SeparationSpace]. ∀[f,g,h:Point(Path(X))]. (path-comp-rel(X;f;g;h) ∈ ℙ)
Proof
Definitions occuring in Statement :
path-comp-rel: path-comp-rel(X;f;g;h),
path-ss: Path(X),
ss-point: Point(ss),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
path-comp-rel: path-comp-rel(X;f;g;h),
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
and: P ∧ Q,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
so_lambda: λ2x.t[x],
cand: A c∧ B,
nat_plus: ℕ+,
uiff: uiff(P;Q),
le: A ≤ B,
false: False,
not: ¬A,
so_apply: x[s],
rdiv: (x/y),
req_int_terms: t1 ≡ t2
Lemmas referenced :
member_rccint_lemma,
all_wf,
real_wf,
rleq_wf,
int-to-real_wf,
rdiv_wf,
rless-int,
rless_wf,
ss-eq_wf,
path-at_wf,
rleq-int-fractions3,
less_than_wf,
false_wf,
rleq_transitivity,
rmul-nonneg-case1,
rleq-int,
rmul_preserves_rleq2,
rmul_wf,
rleq-int-fractions2,
rsub_wf,
ss-point_wf,
path-ss_wf,
separation-space_wf,
rmul_comm,
rinv_wf2,
itermSubtract_wf,
itermMultiply_wf,
itermConstant_wf,
itermVar_wf,
req-iff-rsub-is-0,
rleq-implies-rleq,
rleq_functionality,
req_transitivity,
rmul-rinv,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_mul_lemma,
real_term_value_const_lemma,
real_term_value_var_lemma,
rmul-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
productEquality,
isectElimination,
setEquality,
natural_numberEquality,
hypothesisEquality,
because_Cache,
independent_isectElimination,
inrFormation,
productElimination,
independent_functionElimination,
independent_pairFormation,
imageMemberEquality,
baseClosed,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
dependent_set_memberEquality,
multiplyEquality,
promote_hyp,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
approximateComputation,
int_eqEquality,
intEquality
Latex:
\mforall{}[X:SeparationSpace]. \mforall{}[f,g,h:Point(Path(X))]. (path-comp-rel(X;f;g;h) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-PM-01_20_42
Last ObjectModification:
2018_06_29-PM-05_47_44
Theory : intuitionistic!topology
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