Nuprl Lemma : VesleySchema2_wf
VesleySchema2 ∈ ℙ'
Proof
Definitions occuring in Statement :
VesleySchema2: VesleySchema2,
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
VesleySchema2: VesleySchema2,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
nat_plus: ℕ+,
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
less_than: a < b,
squash: ↓T,
true: True
Lemmas referenced :
all_wf,
nat_plus_wf,
exists_wf,
not_wf,
equal_wf,
int_seg_wf,
subtype_rel_dep_function,
int_seg_subtype_nat_plus,
false_wf,
subtype_rel_self,
regularize_wf,
less_than_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
applyEquality,
lambdaEquality,
cumulativity,
hypothesisEquality,
universeEquality,
intEquality,
because_Cache,
setEquality,
functionExtensionality,
lambdaFormation,
setElimination,
rename,
natural_numberEquality,
independent_isectElimination,
independent_pairFormation,
dependent_set_memberEquality,
imageMemberEquality,
baseClosed
Latex:
VesleySchema2 \mmember{} \mBbbP{}'
Date html generated:
2017_10_03-AM-10_14_46
Last ObjectModification:
2017_09_19-PM-03_52_12
Theory : reals
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