Nuprl Lemma : test-false?_wf
∀[x:test-prop()]. (test-false?(x) ∈ 𝔹)
Proof
Definitions occuring in Statement :
test-false?: test-false?(x),
test-prop: test-prop(),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
test-false?: test-false?(x),
all: ∀x:A. B[x]
Lemmas referenced :
eq_atom_wf,
test-label_wf,
test-prop-obj_wf,
test-prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
tokenEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType
Latex:
\mforall{}[x:test-prop()]. (test-false?(x) \mmember{} \mBbbB{})
Date html generated:
2019_10_15-AM-10_49_53
Last ObjectModification:
2019_03_25-PM-01_48_26
Theory : tree_1
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