### Nuprl Lemma : assert_functionality_wrt_uiff

`∀[u,v:𝔹].  {uiff(↑u;↑v)} supposing u = v`

Proof

Definitions occuring in Statement :  assert: `↑b` bool: `𝔹` uiff: `uiff(P;Q)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` guard: `{T}` equal: `s = t ∈ T`
Definitions unfolded in proof :  guard: `{T}` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` uiff: `uiff(P;Q)` and: `P ∧ Q` sq_type: `SQType(T)` all: `∀x:A. B[x]` implies: `P `` Q` prop: `ℙ`
Lemmas referenced :  subtype_base_sq bool_wf bool_subtype_base assert_witness assert_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut independent_pairFormation thin instantiate lemma_by_obid sqequalHypSubstitution isectElimination cumulativity hypothesis independent_isectElimination equalitySymmetry dependent_functionElimination hypothesisEquality independent_functionElimination productElimination independent_pairEquality isect_memberEquality because_Cache equalityTransitivity

Latex:
\mforall{}[u,v:\mBbbB{}].    \{uiff(\muparrow{}u;\muparrow{}v)\}  supposing  u  =  v

Date html generated: 2016_05_13-PM-03_56_23
Last ObjectModification: 2015_12_26-AM-10_52_19

Theory : bool_1

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