Nuprl Lemma : test-foo-obj_wf
∀x:test-foo(). (test-foo-obj(x) ∈ test-Obj())
Proof
Definitions occuring in Statement :
test-foo-obj: test-foo-obj(x),
test-foo: test-foo(),
test-Obj: test-Obj(),
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
test-Obj: test-Obj(),
test-foo-obj: test-foo-obj(x),
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
test-foo: test-foo(),
subtype_rel: A ⊆r B
Lemmas referenced :
mobj-ext,
test-Spec_wf,
mrec_wf,
test-foo_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
productElimination,
dependent_pairEquality_alt,
tokenEquality,
hypothesisEquality,
universeIsType,
applyEquality
Latex:
\mforall{}x:test-foo(). (test-foo-obj(x) \mmember{} test-Obj())
Date html generated:
2019_10_15-AM-10_48_20
Last ObjectModification:
2019_03_25-PM-01_47_45
Theory : tree_1
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