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,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ,
implies: P ⇒ Q
Lemmas referenced :
istype-universe,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
Error :isect_memberEquality_alt,
Error :universeIsType,
universeEquality,
hypothesis,
Error :inhabitedIsType,
hypothesisEquality,
Error :isectIsType,
Error :functionIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
Error :functionExtensionality_alt,
setEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyEquality,
Error :dependent_set_memberEquality_alt,
Error :equalityIsType1,
setElimination,
rename,
dependent_functionElimination,
independent_functionElimination,
independent_pairFormation,
productElimination
Latex:
\mforall{}f,g:\mcap{}T:Type. (T {}\mrightarrow{} T). (f = g)
Date html generated:
2019_06_20-PM-02_44_01
Last ObjectModification:
2018_10_06-AM-11_24_35
Theory : num_thy_1
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