Nuprl Lemma : polymorphic-id-unique
∀f,g:⋂T:Type. (T ⟶ T). (f = g ∈ (⋂T:Type. (T ⟶ T)))
Proof
Definitions occuring in Statement :
all: ∀x:A. B[x],
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
equal_wf,
set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
isect_memberEquality,
universeEquality,
hypothesis,
isectEquality,
cumulativity,
functionEquality,
hypothesisEquality,
functionExtensionality,
isectElimination,
setEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
thin,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyEquality,
dependent_set_memberEquality,
sqequalRule,
lambdaEquality,
setElimination,
rename,
addLevel,
levelHypothesis,
dependent_functionElimination,
independent_functionElimination,
independent_pairFormation,
productElimination
Latex:
\mforall{}f,g:\mcap{}T:Type. (T {}\mrightarrow{} T). (f = g)
Date html generated:
2017_10_01-AM-09_07_11
Last ObjectModification:
2017_07_26-PM-04_46_44
Theory : general
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