Nuprl Lemma : req*_weakening
∀[x,y:ℝ*]. x = y supposing x = y ∈ ℝ*
Proof
Definitions occuring in Statement :
req*: x = y,
real*: ℝ*,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
req*: x = y,
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
all: ∀x:A. B[x],
real*: ℝ*,
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
req*_wf,
squash_wf,
true_wf,
iff_weakening_equal,
false_wf,
le_wf,
req_weakening,
subtype_rel_self,
nat_wf,
req_witness,
int_upper_wf,
all_wf,
req_wf,
int_upper_subtype_nat,
equal_wf,
real*_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
axiomEquality,
hypothesis,
thin,
rename,
applyEquality,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_pairFormation,
dependent_set_memberEquality,
independent_pairFormation,
lambdaFormation,
setElimination
Latex:
\mforall{}[x,y:\mBbbR{}*]. x = y supposing x = y
Date html generated:
2018_05_22-PM-03_14_13
Last ObjectModification:
2017_10_06-PM-02_00_13
Theory : reals_2
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